Related papers: Efficient Computation of Higher-Order Variational …
Algorithms that use derivatives of governing equations have accelerated rigid robot simulations and improved their accuracy, enabling the modeling of complex, real-world capabilities. However, extending these methods to soft and hybrid…
We present an algorithm for the rapid numerical integration of smooth, time-periodic differential equations with small nonlinearity, particularly suited to problems with small dissipation. The emphasis is on speed without compromising…
Scientific studies often require the precise calculation of derivatives. In many cases an analytical calculation is not feasible and one resorts to evaluating derivatives numerically. These are error-prone, especially for higher-order…
In this work, the benefits of the phase fitting technique are embedded in high order discrete Lagrangian integrators. The proposed methodology creates integrators with zero phase lag in a test Lagrangian in a similar way used in phase…
In this paper, we present a novel approach to efficiently generate collision-free optimal trajectories for multiple non-holonomic mobile robots in obstacle-rich environments. Our approach first employs a graph-based multi-agent path planner…
Metropolitan scale vehicular traffic modeling is used by a variety of private and public sector urban mobility stakeholders to inform the design and operations of road networks. High-resolution stochastic traffic simulators are increasingly…
A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…
Taylor series methods show a newfound promise for the solution of non-stiff ordinary differential equations (ODEs) given the rise of new compiler-enhanced techniques for calculating high order derivatives. In this paper we detail a new…
Motion trajectory planning is one crucial aspect for automated vehicles, as it governs the own future behavior in a dynamically changing environment. A good utilization of a vehicle's characteristics requires the consideration of the…
Simulation of contact and friction dynamics is an important basis for control- and learning-based algorithms. However, the numerical difficulties of contact interactions pose a challenge for robust and efficient simulators. A…
This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…
This contribution proposes a new formulation to efficiently compute directional derivatives of order one to fourth. The formulation is based on automatic differentiation implemented with dual numbers. Directional derivatives are particular…
We propose a family of reliable symplectic integrators adapted to the Discrete Non-Linear Schr\"odinger equation; based on an idea of Yoshida (H. Yoshida, Construction of higher order symplectic integrators, Physics Letters A, 150, 5,6,7,…
We construct numerical integrators for Hamiltonian problems that may advantageously replace the standard Verlet time-stepper within Hybrid Monte Carlo and related simulations. Past attempts have often aimed at boosting the order of accuracy…
We present a novel second-order trajectory optimization algorithm based on Stein Variational Newton's Method and Maximum Entropy Differential Dynamic Programming. The proposed algorithm, called Stein Variational Differential Dynamic…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
We introduce a variational algorithm to estimate the likelihood of a rare event within a nonequilibrium molecular dynamics simulation through the evaluation of an optimal control force. Optimization of a control force within a chosen basis…
We proposed an algorithm for solving Hamilton-Jacobi equation associated to an optimal trajectory problem for a vehicle moving inside the pre-specified domain with the speed depending upon the direction of the motion and current position of…
We propose a simple quantum algorithm for simulating highly oscillatory quantum dynamics, which does not require complicated quantum control logic for handling time-ordering operators. To our knowledge, this is the first quantum algorithm…
Real-world physics can only be analytically modeled with a certain level of precision for modern intricate robotic systems. As a result, tracking aggressive trajectories accurately could be challenging due to the existence of residual…